Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The volume of a rectangular solid is $210 \mathrm{cm}^{3}$ and the surface area is $214 \mathrm{cm}^{2}$. If the area of the base is$42 \mathrm{cm}^{2}$, then the edges of the rectangular solid are
(a)3, 4 and 5 cm
(b)4, 5 and 6 cm
(c)5, 6 and 7 cm
(d)6, 6 and 8 cm
Answer
Answer (as printed): C
Explanation
Let $l, b$ and $h$ represent the lengths of the edges of the solid. Then, $l \times b=42$ $$l b h=210 \Rightarrow h=\frac{210}{l b}=\frac{210}{42} \Rightarrow h=5 .$$ Surface area $=2(l b+b h+l h)=2(42+5 b+5 l)$ $$=84+10(l+b) . \therefore 84+10(l+b)=214 \Rightarrow l+b=13 .$$ Putting $b=(13-l)$ in (i), we get: $l(13-l)=42 \Rightarrow l^{2}-13 l$ $+42=0 \Rightarrow(l-6)(l-7)=0$ $\Rightarrow l=7$. Hence, length $=7 \mathrm{cm}$, breadth $=6 \mathrm{cm}$, height $=5 \mathrm{cm}$.